OBJECTIVE_VEC_HARDMIXVAF - calculates the objective minimization function

Comments

This function defines the objective function that depends on the given data and on theta. Note that the function does not return a scalar but a vector. The Matlab build-in optimizer (e.g., lsqnonlin) minimizes the sum of squared entries of this vector.

This function may be converted into a Matlab executable file (.mex file) with the Matlab Coder to accelerate the objective function evaluation.

Input Arguments

paramters (double) - material parameters

q_case (double) - see opt_input documentation

q (double) - see opt_input documentation

lambda_r (double) - see opt_input documentation

lambda_p (double) - see opt_input documentation

p (double) - see opt_input documentation

n_eval (double) - see opt_input documentation

u (double) - displacement data for every load step (every column corresponds to one load step)

reaction (double) - reaction force data for every load step

n_NR_local (double) - maximum number of Newton-Raphson iterations used for solving the local problem (return mapping algorithm)

tol_NR_local (double) - stopping tolerance for the Newton-Raphson iteration used for solving the local problem (return mapping algorithm)

CPlaneStress (double) - known elastic properties (stiffness matrix)

SPlaneStress (double) - known elastic properties (compliance matrix)

n_dof (double) - number of degrees of freedom in the mesh

n_element (double) - number of finite elements in the mesh

n_dof_per_element (double) - number of degrees of freedom per finite element

element_dof (double) - degrees of freedom at each finite element element (each row provides all degrees of freedom at the corresponding finite element)

Gauss_weights (double) - Gaussian quadrature weights

n_Gauss_per_dim (double) - number of Gauss points per dimension

detJ_GP (double) - determinant of the Jacobian at each Gauss point needed for mapping integrals between the reference and physical finite element

B_GP (double) - help matrix at each Gauss point needed for calculating shape function derivatives

dof_free (double) - free degrees of freedom

dof_reaction (double) - degrees of freedom corresponding to reaction forces

Output Arguments

cost (double) - vector, whose sum of squared entries must be minimized (note that the regularization term is included as the last entry of this vector)